We show that the Yao graph Y 4 in the L 2 metric is a spanner with stretch factor 8 √ 2(29+ 23 √ 2). Enroute to this, we also show that the Yao graph Y ∞ 4 in the L∞ metric is a plane spanner with stretch factor 8.
We show that, for any integer k ≥ 6, the Sparse-Yao graph Y Y 6k (also known as Yao-Yao) is a spanner with stretch factor 11.67. The stretch factor drops down to 4.75 for k ≥ 8.
We introduce the problem of <i>shape replication</i> in the Wang tile self-assembly model. Given an input shape, we consider the problem of designing a self-assembly system which will replicate that shape into either a specific number of copies, or an unbounded number of copies. Motivated by practical DNA implementations of Wang tiles, we consider a model… (More)
Let S and T be two sets of points with total cardinality n. The minimum-cost many-to-many matching problem matches each point in S to at least one point in T and each point in T to at least one point in S, such that sum of the matching costs is minimized. Here we examine the special case where both S and T lie on the line and the cost of matching s ∈ S to t… (More)
For a set of points in the plane and a fixed integer k > 0, the Yao graph Yk partitions the space around each point into k equiangular cones of angle &thetas; = 2π/k, and connects each point to a nearest neighbor in each cone. It is known for all Yao graphs, with the sole exception of Y5, whether or not they are geometric spanners. In this paper we… (More)
This paper presents a distributed algorithm that runs on an n-node unit ball graph (UBG) G residing in a metric space of constant doubling dimension, and constructs, for any ε > 0, a (1 + ε)-spanner H of G with maximum degree bounded above by a constant. In addition, we show that H is " lightweight " , in the following sense. Let ∆ denote the aspect ratio… (More)
It is a standing open question to decide whether the Yao-Yao structure for unit disk graphs (UDGs) is a length spanner of not. This question is highly relevant to the topology control problem for wireless ad hoc networks. In this paper we make progress towards resolving this question by showing that the Yao-Yao structure is a length spanner for UDGs of… (More)